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 Localization of cohomological induction

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We give a geometric realization of cohomologically induced g,K-modules. Let h,L be a subpair of g,K. The cohomological induction is an algebraic construction of g,K-modules from a h,L-module V. For a real semisimple Lie group, the duality theorem by Hecht, Milicic, Schmid, and Wolf relates g,K-modules cohomologically induced from a Borel subalgebra with D-modules on the flag variety of g. In this article we extend the theorem for more general pairs g,K and h,L. We consider the tensor product of a D-module and a certain module associated with V, and prove that its sheaf cohomology groups are isomorphic to cohomologically induced modules.

Author: Yoshiki Oshima

Source: https://archive.org/


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